ENSAE Paris - École d'ingénieurs pour l'économie, la data science, la finance et l'actuariat

Méthodes numériques en ingénierie financière


Participants of this course will master computational techniques frequently used in mathematical finance applications.


Prerequisites: Stochastic processes / stochastic calculus, Numerical Analysis, Derivatives, Command of Python

TDs: In the form of ipython notebooks


1. Brief introduction to asset price modeling and option pricing

  • Basic stochastic models in finance
  • Overview of numerical methods for option pricing

2. Monte Carlo methods for pricing

  • Basics of MC simulation and price estimation in the Black-Scholes Model
  • Variance reduction techniques
  • Euler schemes and applications to pricing in local volatility models
  • Computing greeks

3. Option pricing via PDEs

  • Finite difference approximation of Black-Scholes PDE
  • American options and free boundary problems

4. Transformation based methods

  • Affine models
  • Option pricing via Fourier transforms

5. Probabilistic numerical methods for non-linear pricing

  • American options (Tsitsiklis-Van Roy, Longstaff-Schwarz methods)
  • Market with imperfections and non-linear pricing (BSDEs)
  • Dynamic programming vs. shooting method (Non linear regression)


·      Achdou, Yves; Pironneau, Olivier. Computational methods for option pricing. Frontiers in Applied Mathematics, 30. SIAM, Philadelphia, PA, 2005.

·      Björk, Tomas. Arbitrage theory in continuous time. Third edition, OUP Oxford, 2009.

·      Gatheral,  Jim. Volatility Surface: A Practitioner’s Guide. Wiley, 2006.

·      Glasserman, Paul. Monte Carlo methods in financial engineering. Springer, 2003.

·      Hilber, Norbert; Reichmann, Oleg; Schwab, Christoph; Winter, Christoph. Computational methods for quantitative finance. Springer, 2013.

·      Hirsa, Ali. Computational methods in finance. Chapman & Hall/CRC Financial Mathematics Series. CRC Press, Boca Raton, FL, 2013.

·      Lamberton, Damien; Lapeyre, Bernard. Introduction to stochastic calculus applied to finance. Second revised edition. Chapman & Hall/CRC, 2008.

·      Seydel, Rüdiger U. Tools for computational finance. Fourth edition. Universitext. Springer-Verlag, Berlin, 2009.

·      Shreve, Steven E. Stochastic calculus for finance II: Continuous-Time models, Volume 11. Springer Science & Business Media, 2004.

·      Additional lecture material will be provided by the instructors.